Download Adding It All Up Lesson Plan Form - SUCCESS-OBR

Tiered Lesson (Nancy Plavan and Jill Madonia)
(Adapted from the NCTM Illuminations website: http://illuminations.nctm.org/LessonDetail.aspx?id=L765)
Grade Level: 6
Title of Lesson: Adding It All Up
Time Frame: 50 minutes
Objectives
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Ohio Academic Standard(s):
Investigate the pattern between the number of sides of a polygon and
the sum of the interior angles using in two different methods
Determine that the interior angle sum is always the same for polygons
with the same number of sides
Create a formula to find the interior angle sum given the number of
sides
Explore interior angles in regular polygons
Tier I:
Working in homogeneous groups based on their
ability to access the problem, all students will
explore the relationship between the number of
sides of a polygon and the sum of their interior
angles using the Angle Sum Applet from the
Illuminations website. Students will share their
observations with the whole class.
Working with partners, all students will draw
polygons, divide the polygons into non-overlapping
triangles, and complete the table and Table
Questions 1 – 4, and Triangulation Questions 1 – 4,
provided in the Adding It All Up Activity sheet.
Students will share out table entries and answers.
Tier I students should be given the first opportunity
to respond. Discussion should include students’
thinking and strategies for finding the angle
sums…especially sums for polygons with greater
numbers of sides.
Geometry 6-8
1. Understand relationships among the angles, side lengths, perimeters,
areas, and volumes of similar objects
2. Draw geometric objects with specified properties, such as side lengths
or angle measures.
Measurement 6-8
1. Develop and use formulas to determine the circumference of circles
and the area of triangles, parallelograms, trapezoids, and circles and
develop strategies to find the area of more-complex shapes.
Tier II:
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As the students are working, the teacher will
1.
circulate around the room asking probing questions
in an effort to get each group to talk about what
they are discovering through their work.
The teacher will differentiate by choosing each
group to share out responses to the questions that
(s)he feels they will be most comfortable discussing
2.
based on their entry level into the problem.
3.
Tier III:
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Students will be given the opportunity to explore
exterior angles with the goal of finding the
exterior angle sum and the measure of each
individual exterior angle if the polygon is
regular. (The sum of the exterior angles for any
polygon is 360°, and therefore the measure of
one exterior angle in a regular polygon is 360/n ).
In the bottom right-hand corner of the Angle
Sum applet, there is an animation for the triangle
and square showing how the sum of the interior
angles relates to tiling. Have students watch the
animations and write a journal entry on what
they demonstrate.
Vocabulary:
polygon, regular polygon, non-regular polygon,
pentagon, hexagon, heptagon, octagon, nonagon, decagon, n-gon,
convex, concave, triangulation
Material List
Unlined paper, rulers, colored pencils,
“Adding It All Up” activity sheet handout and key
Computers/internet (if only one computer is available, then the teacher can facilitate a large group discussion using the Angle-Sum Applet)
Angle Sum Applet (Illuminations.nctm.org)
Assessment
1. Ongoing assessment will take place as the teacher monitors the activity and engages in discussion with the students in individual groups.
2. Create a set of cards numbered from 50 to 100. Randomly give 1 card to each student. Ask all students to find the sum of the interior angles of a polygon with
the number of sides shown on their card and the measure of 1 interior angle of a regular polygon with that same number of sides.
Additional Accommodations and/or Modifications